it would be greatly appreciated if someone could help me.

The value of [tex]P$$(2 < x < 10)$[/tex] is 0.5350

As per the Function, [tex]$P(x < x)=1-e^{-m x}$[/tex]

Where [tex]$x \sim E x p(0.2)$[/tex]

Therefore, [tex]$m=0.2$[/tex]

[tex]$$P(2 < x < 10)=P(x < 10)-P(x < 2)$$[/tex]

Applying all data

[tex]& \mathrm{P}\left(2 < \mathrm{x} < 10=\left(1-e^{0.2 \times 10}\right)-\left(1-e^{0.2 \times 2}\right)\right. \\[/tex]

=0.6703-0.1353=0.5350

The complete question is,

A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be

modelled by the following distribution: X-Exp(0.2)

Find [tex]$P(2 < x < 10)$[/tex].

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It is discovered that the phrase under the division symbol is 3x2 - (b - 2)x - c, meaning that b = 5 and c = 3.

find the roots of  x2 - x - 1  =  0    

--->     Using the quadratic formula, the roots are  [ 1 + sqrt(5) ] / 2   and   [ 1 + sqrt(5) ] / 2.

Placing these values into the equation  x5 - bx - c  =  0,  we get:

x  =  [ 1 + sqrt(5) ] / 2   --->   ( [ 1 + sqrt(5) ] / 2 )5   -  b( [ 1 + sqrt(5) ] / 2 )  -  c  =  0

--->    [ 176 + 80sqrt(5) ] / 32  -  ( [ 1 + sqrt(5) ] / 2 )b  -  c  =  0

multiplying by 32     --->    176  +  80sqrt(5)  -  16b  -  16sqrt(5)b  -  32c  =  0

Using the same steps for x  =  [ 1 - sqrt(5) ] / 2 , we get:     176  -  80sqrt(5)  -  16b  +  16sqrt(5)b  -  32c  =  0

Now, let's combine these two results:      176  +  80sqrt(5)  -  16b  -  16sqrt(5)b  -  32c  =  0

   176  -  80sqrt(5)  -  16b  +  16sqrt(5)b  -  32c  =  0

Subtract the lower equation from the upper:      160sqrt(5)  -  32sqrt(5)b  =  0   --->     160sqrt(5)  =  32sqrt(5)b     --->     b  =  5

Now, substitute this value for b into  176  +  80sqrt(5)  -  16b  -  16sqrt(5)b  -  32c  =  0

--->176  +  80sqrt(5)  -  16(5)  -  16sqrt(5)(5)  -  32c  =  0    

--->176  +  80sqrt(5)   - 80  -  80sqrt(5)  - 32c  =  0

--->96  -  32c  =  0

--->c  =  3

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Answer:

FV = $1,200 * e^(0.09*10)

Step-by-step explanation:

The equation used to calculate the future value of an investment compounded continuously is:

FV = PV * e^(r*t)

where:

FV = future value

PV = present value (initial investment) = $1,200

r = annual interest rate (9% = 0.09)

t = number of years (10 years)

So, the future value of the investment would be:

FV = $1,200 * e^(0.09*10)

The change in elevation of the scuba diver after 8 minutes is -24.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers. Unknown variables, numbers, and arithmetic operators make up an algebraic expression. It contains no equality or inequality symbols.

The expression (8)(2)(-1.5) represents the change in the scuba diver's elevation after 8 minutes.

To determine the change in elevation, we need to evaluate the expression.

(8)(2)(-1.5) = (16)(-1.5) = -24

Thus, the change in elevation is -24.

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Thomas invested $3,000 into a bank account with a 5% interest return compounded annually. then the following equations indicates the total amount of money 3000(1.05)^1/16

Thomas invested $3,000 into a bank account with a 5% return compounded annually.

A: represents the current balance or compound amount in the account.

P: represents the principal (the original amount deposited).

R: annual interest rate (in decimal form).N: the number of times per year that interest is compounded .T: time in years the money has been invested.

The formula of interest is A=P (1+r)ⁿ

A=Final amount  

P= Principal ( deposit invested)  

r= interest rate

n= time

So,  in this case

P=$3,000

r= 5% or 0.05

n=1/ 16

Replacing

A=3000(1+0.05)^1/16

A=3000( 1.05)^1/16

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Answer :

0.783

Step-by-step explanation:

We know that,

sin^2 (x) + cos^2 (x) = 1

Thus,

[tex] \sin^{2} (A) + cos^{2} (A) = 1 \\ cos^{2} A =1 - sin^{2} A \\ cos^{2} A = 1 - (0.622)^{2 } \\ cos^{2} A = 1 - 0.386884 \\ cos A = \sqrt{0.613116} \\ = 0.783[/tex]

Answer: 3,-5

Step-by-step explanation:

Answer: (3, -5)

......................................

Scale of the model is found to be 1 : 30 using the ratio method.

A model of a car is 4 inches long.

The actual car is 10 feet long.

 4 in. = 10 ft. ( since given )

Divide both sides by 4, we get

∴ 1 in. = 2.5 ft.

We use the ratio here to compare the lengths of the actual car and its model.

A ratio scale is a quantitative measurement scale that is used to compare numbers.

The model is 4 inches long while the actual car is 10 feet long.

One foot is equal to 12 inches. Therefore the car in terms of inches is:

10 feet × 12 inches = 120 inches

The ratio scale is the length of the model of the car : length of the actual car

= 4 : 120

= 1 : 30

Therefore the scale of the model is 1: 30.

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Answer:

$1.92

Step-by-step explanation:

$11.59 - $9.67 = $1.92

An equation that represents the number of miles, m, Enrique walks in w weeks will be N = 32T.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that every week, Enrique walks one mile each day for 4 days a week. He can usually walk 1 mile in about 14 to 16 minutes. Estimate the number of minutes Enrique will spend walking over an 8-week period.

The expression for the total time will be calculated as:-

N = 32 x T

Here, T is the time in minutes for running per mile.

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Answer: A

Step-by-step explanation:

Present value of F (P) = Compound amount (F) (1+periodic rate)

The student's final grade is 78.9.

The final grade of the student is determined using the weight average. A weighted average refers to a type of mean that gives differing importance to the values in a dataset. It is used when the relative significance of values in a dataset are to be considered. The formula for finding the weighted average is the sum of all the variables multiplied by their weight, then divided by the sum of the weights.

Based on the provided information, as student score 84 on quizzes with weighted 30%, 72 on exams with weighted 40%, and 83 on final exam with weighted 30%, hence

Final grade = (84*0.3 + 72*0.4 + 83* 0.3)/(0.3 + 0.4 + 0.3) = (25.2 + 28.8 + 24.9)/1 = 78.9

Note: The question is incomplete. The complete question probably is: For a chemistry class, a student's grades are weighted as follows: quizzes are 30%, exams are 40%, and the final exam is 30%. If a student scored 84, 72, and 83 on the quizzes, exams, and final respectively, calculate the student's final grade. express your answer to three significant figures.

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Answer:

79.6

Step-by-step explanation:

(86x.3)+(73x.4)+(82x.3)

For a family of linear functions with slope 2, the equation is y = 2x + b, where b is the y-intercept. For a family of linear functions such that f(2) = 1, the equation is y = x + b, where b is the y-intercept. Both families of linear functions have the same equation, y = x + b, and all functions belonging to both families have a slope of 1 and a y-intercept of b.

(a) The equation for the family of linear functions with slope 2 is y = 2x + b, where b is the y-intercept. To sketch several members of the family, plot several points (x, y) with the equation, then connect the points to form a line.

(b) The equation for the family of linear functions such that f(2) = 1 is y = x + b, where b is the y-intercept. To sketch several members of the family, plot several points (x, y) with the equation, then connect the points to form a line.

(c) The equation for both families of linear functions is y = x + b, where b is the y-intercept. All functions belonging to both families have a slope of 1 and a y-intercept of b.

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The Equation of the line which has a slope of 1/5 and passes through (-10,4) will be  [tex]y = \frac{1}{5} x + 6[/tex] .

Given, We have the slope of the line = 1/5 and a  point (-10,4) though which the line passes. We know that the form of a linear line is y=mx + c (slope intercept form) where m is the gradient/slope of the line and c is the point where it intercepts the y axis on the graph. We can directly put the value slope in the place of m.

To find C , we can put the coordinates of the given point in the equation to solve for C. Therefore :

⇒ y = mx + c

⇒y =  1/5 x + c

⇒4 = 1/5 x (-10) + c

⇒4 = -2 + c

⇒ 4 +2 = c

⇒c =  6

Putting all the values in equation gives us the linear equation of the line :  [tex]y = \frac{1}{5} x + 6[/tex]

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The complete question is :

What is the locus/ linear equation/ equation of the line that has a slope of 1/5 and passes through coordinates (-10,4)?

Mary owes $13564 income tax.

Governments apply income taxes as a sort of tax on the income produced by people and businesses under their control. Government duties, public services, and citizen goods are all paid for through income tax revenue.

Given that the taxable income is $68,562.

Income tax is the tax charged on an individual's or entity's income

Using the table as a guide, $68,562 falls within the income range $31,850 - $77,100

So, the tax is $4386 added to 25% of the excess over $31850

This is calculated as:

tax = $4386 + 25%(income - 31,850)

In our case,

income = $68562

Substitute $68,562 for income

Tax = $4386 + 25%(68,562 - 31,850)

Solve the expression in the bracket

tax = 4386 + 9178

Add the terms of the expression

tax = 13,564

therefore, Mary owes $13564 in income tax.

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The rebound velocity of the ball, vfx, is 10.0 m/s, calculated using the equation vfx = 2vix - viy, where vix is the initial velocity along the x-axis (4.0 m/s) and viy is the initial velocity along the y-axis (-2.0 m/s).

Using the equation vfx = 2vix - viy, the rebound velocity of the ball is calculated as follows:

vfx = 2(4.0 m/s) - (-2.0 m/s) = 10.0 m/s

1. Identify the initial velocity, vix, of the ball along the x-axis, which is 4.0 m/s.

2. Identify the initial velocity, viy, of the ball along the y-axis, which is -2.0 m/s.

3. Use the equation vfx = 2vix - viy to calculate the rebound velocity of the ball, vfx.

4. Calculate vfx = 2(4.0 m/s) - (-2.0 m/s) = 10.0 m/s.

The rebound velocity of the ball is 10.0 m/s.

The rebound velocity of the ball, vfx, is 10.0 m/s, calculated using the equation vfx = 2vix - viy, where vix is the initial velocity along the x-axis (4.0 m/s) and viy is the initial velocity along the y-axis (-2.0 m/s).

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The word used incorrectly in the sentence is "envelopes".

The word used incorrectly in the sentence is "envelopes". The comment should be "envelopes" instead. This is because "envelopes" is a plural noun, referring to more than one envelope. The apostrophe in "envelopes" implies possession, indicating that the envelopes belong to someone or something, but it is not necessary for this context.

Hence, the correct sentence should be "The mailperson's job is to put the envelopes in every mailbox on the block."

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Answer:

x = 3

Step-by-step explanation:

3|x|- 1= 8

=3x = 8 + 1

=3x = 9

=3x/3 = 9/3

x = 3.

Answer:

The equation is 3|x| - 1 = 8. To solve this equation, we first need to consider the absolute value of x.

The absolute value of x is defined as |x| = x for x ≥ 0, and |x| = -x for x < 0.

We have 3|x| - 1 = 8, so we have to consider two cases:

x ≥ 0: in this case, |x| = x and we have 3x - 1 = 8, which gives x = 3 or x = 9.

x < 0: in this case, |x| = -x and we have 3(-x) - 1 = 8, which gives -3x - 1 = 8, and then x = -3 or x = -9.

So the solution to the equation is x = 3 or 9 or x = -3 or -9.

Step-by-step explanation:

The missing part of the equation should be like 1000 g / 1 kg × 100 cm / 1 m

Given,

The set of units used in the final response is different. In particular, kilogram (kg) and meters (m) are converted to gramm(g) and centimeter (cm), respectively (cm). You must multiply the initial value by proportions to achieve this adjustment.

It is crucial to organize these proportions in a way that permits unit cancellation when writing them down. As an illustration, since kg and m are both in the numerator, they must be in the denominators of the conversions.

Proportions:

1 kg = 1,000 g

1 m = 100 cm

Here,

The complete equation is like;

-4.3 × 10⁴ (kg × m / s) × (1000 g / 1 kg) × (100 cm / 1 m) = ? (g × cm / s)

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Complete question is attached

a) The first four nonzero terms of the Taylor series are 3, -3t^2, 3/3t^4, -3/5t^6

b) The first four nonzero terms of the power series expansion of g(x) about x=0 are 3x, -x^3, 3/5x^5, -3/7x^7.

c) The interval of convergence for the power series of g(x) is (-sqrt(5/3), sqrt(5/3)).

What is a function?

A function is a mathematical relationship between two variables, often denoted as "f(x)" or "y = f(x)". A function assigns a unique output to each input within its domain. In other words, for every value of x, there is a corresponding value of y, and each value of x can only correspond to one value of y.

a. To find the first four nonzero terms and the general term for the power series expansion of f(t) about t=0, we need to find the Taylor series of f(t) centered at 0. The general term of a Taylor series is given by:

f(t)^(n) / n! * (t-0)^n

The Taylor series of f(t) = 3/(1+t^2) centered at 0 is:

f(t) = 3 - 3t^2 + 3/3t^4 - 3/5t^6 + ...

The first four nonzero terms of the Taylor series are 3, -3t^2, 3/3t^4, -3/5t^6

b. To find the first four nonzero terms and the general term for the power series expansion of g(x) = ∫f(t)dt about x=0, we need to integrate the Taylor series of f(t) term by term.

g(x) = ∫f(t)dt = (3t - 3/3t^3 + 3/5t^5 - ...) from 0 to x

g(x) = 3x - 3/3x^3 + 3/5x^5 - ...

The first four nonzero terms of the power series expansion of g(x) about x=0 are 3x, -x^3, 3/5x^5, -3/7x^7

c. The interval of convergence of a power series is the set of values of x for which the series converges. To find the interval of convergence for g(x), we can use the ratio test.

The ratio test states that if the limit of |a(n+1)x^(n+1)|/|a(n)x^n| as n approaches infinity is less than 1, the series converges for all x.

|3/7x^7|/(|3/5x^5|) = |x^2|/(|3/5|) < 1 when |x| < sqrt(5/3)

So, the interval of convergence for the power series of g(x) is (-sqrt(5/3), sqrt(5/3)).

Hence,

a) The first four nonzero terms of the Taylor series are 3, -3t^2, 3/3t^4, -3/5t^6

b) The first four nonzero terms of the power series expansion of g(x) about x=0 are 3x, -x^3, 3/5x^5, -3/7x^7.

c) The interval of convergence for the power series of g(x) is (-sqrt(5/3), sqrt(5/3)).

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Answer:

it analyses how citizenship was different in the past

Correlation: A correlation is a statement that suggests there is a relationship between two variables, where a change in one variable tends to follow or be associated with a change in another variable.

A correlation is a statement that suggests there is a relationship between two variables. It does not necessarily mean that a change in one variable will cause a change in the other variable, but that a change in one tends to follow or be associated with a change in the other. For example, a correlation could be made between the amount of rainfall a region receives and the number of plants that are able to grow there. If the rainfall increases, then the number of plants that can grow in the region is likely to increase as well. A correlation can be either positive or negative, with a positive correlation meaning that an increase in one variable will likely result in an increase in the other, and a negative correlation meaning that an increase in one variable will likely result in a decrease in the other. Correlation can be used to make predictions, but should not be confused with causation, as correlation does not necessarily imply causation.

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The complete question: which of the following refers to a statement that  there is a relationship between two variables that can change in one variable tends to follow or be associated with a change in another variable?

A Prime factor is a natural number that has only two factors namely 1 and the number itself. One is not a prime number. Prime factors are odd in nature except for 2 because 2 is the only even prime factor. Example of prime factors are 2,3,5,7,11 etc

def print_prime_factors(number):

 factor = 2

 while factor <= number:

   # Check if factor is a divisor of number

   if number % factor == 0:

     # If it is, print it and divide the original number

     print(factor)

     number = number / factor

   else:

     # If it's not, increment the factor by one

    factor+=1

 return "Done"

print_prime_factors(100)

Complete question- Above mentioned is the correct code with all blanks filled.

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The missing value in the solution to the equation is 4. The value of x is 4 and y is -6 which is (4, -6).

A solution to an equation is a value or values that make the equation true. For example, if the equation is x + 3 = 7, then the solution to the equation would be x = 4.

To solve an equation, you must use a combination of addition, subtraction, multiplication, division, and algebraic manipulations to isolate the unknown variable. For instance, to solve the equation x + 3 = 7, you would subtract 3 from both sides of the equation to find x = 4.

It is important to note that an equation may have more than one solution. For example, the equation x2 + 4 = 0 has two solutions, x = 2 and x = -2.

In some cases, equations may not have a solution. This happens when the equation is not true for any value of the unknown variable. For example, the equation 0 = 1 is not true for any value of x, so it does not have a solution.

In summary, a solution to an equation is a value or values that make the equation true. To solve an equation, you must use a combination of addition, subtraction, multiplication, division, and algebraic manipulations to isolate the unknown variable. An equation may have multiple solutions or no solution at all.

The given equation is 4x + y = 10.

We have the value of y is -6,

To find the value of x, using the equation 4x + y = 10

4x - 6 = 10

4x = 10 +6

4x = 16

x = 4

The missing value in solution is 4.

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Answer:

82

Step-by-step explanation:

average class score=total number of test scores/number of test scores

sum up the scores 79+82+85+91+97+73+88+87+85+92+90+85+86+91+94+85+92

=1482÷18=82.33333

=82

Answer: It is 36cm the height of it and the length W times L

Step-by-step explanation:

The function g(16) = -1/2 x + 5 is solved by substitution to get -3

The process of changing an algebraic letter to it's value corresponds to the procedure known as substitution.

In the problem, the equation g(16) = -1/2 x + 5,

Considering the equation, the value of x is 16. The letter x will be replaced by 16 in the equation

g(16) = - 1/2 x + 5

g(16) = - 1/2  * 16 + 5

g(16) = - 8 + 5

g(16) = -3

Substituting x = 16 in the equation g(16) = -1/2 x + 5 results to a solution of -3

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The magnitude of the second earthquake is given as follows:

5.80.

The magnitude of an earthquake is given by the equation presented as follows:

[tex]M = \frac{2}{3}\log{\left(\frac{E}{E_0}\right)}[/tex]

The first earthquake has a magnitude of 3.9, hence it's energy is obtained as follows:

[tex]3.9 = \frac{2}{3}\log{\left(\frac{E}{E_0}\right)}[/tex]

[tex]\log{\left(\frac{E}{E_0}\right)} = \frac{3.9 \times 3}{2}[/tex]

[tex]\log{\left(\frac{E}{E_0}\right)} = 5.85[/tex]

As the power of 10 is the inverse function of the logarithm, we have that:

[tex]\frac{E}{E_0} = 10^5.85[/tex]

[tex]\frac{E}{E_0} = 707946[/tex]

[tex]E = 707946E_0[/tex]

The second earthquake has 700 times as much energy as the first, hence the energy is of:

[tex]E = 700 \times 707946E_0[/tex]

[tex]E = 495562049E_0[/tex]

Then the magnitude of the second earthquake is given as follows:

[tex]M = \frac{2}{3}\log{\left(\frac{495562049E_0}{E_0}\right)}[/tex]

[tex]M = \frac{2}{3}\log{(495562049)}[/tex]

M = 5.80.

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Answer:

-2.5, -2.02, -11/4

Step-by-step explanation:

Any number beginning with -2 will be the answer. -11/4 is -2.75 when converted to a decimal!

Answer:60 percent

Step-by-step explanation:

Step 1) 72 = 120% × Y

Step 2) 72 = 120/100× Y

Multiplying both sides by 100 and dividing both sides of the equation by 120 we will arrive at:

Step 3) Y = 72 × 100/120

Step 4) Y = 72 × 100 ÷ 120

Step 5) Y = 60